1. Field of the Invention
This invention relates to a 90-degree digital phase shift network comprising a plurality of all-pass digital filters, and a method for producing the net-work, and more particularly to a network of this kind capable of obtaining good characteristics in a low-frequency band. Further, the invention relates to a linearizer which employs all-pass digital filters.
2. Description of the Related Art
A 90-degree digital Phase Shift Network (PSN) is widely used in modulation/demodulation processes in the field of communication. In general, the PSN comprises two all-pass digital filters.
Digital filters have digital elements such as an adder, a multiplier, a register, etc., and are mainly sorted into FIR (Finite Impulse Response) digital filters and IIR (Infinite Impulse Response) digital filters, which will be hereinafter called "IIR-DF"s. In the recent years, there has been a tendency to use the IIR-DF as the 90-degree digital PSN, since it can provide high precision even when it incorporates relatively low order filters.
FIG. 1 shows a simple first-order IIR-DF structure.
As is shown in FIG. 1, the IIR-DF comprises an input register (not shown) which stores an input signal x[k], an output register (not shown) which stores an output signal y[k], a coefficient register for holding a filter coefficient b, and an adder. The IIR-DF calculates b.multidot.y[k-1], then adds b.multidot.y[k-1] to the value x[k] of the input register, and stores the addition result in the output register, thus functioning as a first-order digital filter.
There are various types of IIR-DFs, such as a transposition type, a parallel type, and a serial type, and these are used each in its proper way.
The IIR-DF can be realized also in a software manner, that is, by means of a numerically arithmetic program operated in a hardware system such as an LSI (For example DSP: Digital Signal Processor).
The above conventional digital filter will be explained with the use of an n'-order digital filter of a serial type comprising first-order filter connected in series, for easy expansion of formulas. The digital filter of a serial structure comprising first-order filters will be referred to simply as "digital filter".
The digital filter is obtained by calculating a transfer function relating to an analog filter, expressed by the following equation (see, for example, D. K. Weaver, `Design of RC wide-band 90-degree phase-difference network`, Proc. IRE, pp. 671-676, Apr. 1954), then subjecting the calculated transfer function relating to the analog filter to bilinear z-transform to obtain the transfer function relating to the digital filter, and determining the structures of the hardware and software systems employed, on the basis of the obtained function relating to the digital filter. The 90-degree digital PSN comprises digital filters designed on the basis of the calculated transfer functions relating to the digital filters. ##EQU2##
In the above equation, H(s) represents a transfer function relating to an analog filter, n' represents the filter order, and P.sub.i represents the coefficient of the filter, which are all real numbers, and s represents the Laplacean Factor.
Further, there is known a method for producing a 90-degree digital PSN which employs IIR Hilbert transformers. These IIR Hilbert transformers are produced by the use of Remez exchange algorithm (see Masaaki Ikehara, Hiroyuki Tanaka, and Hirohumi Matsuo, `Design of IIR Hilbert Transformers Using Remez Algorithm`, IEICE Vol. J74-A, No. 3, pp. 414-420, Mar. 1992).
However, the obtained 90-degree digital PSN by this method cannot provide a good phase shift characteristics, in particular, in a low-frequency band.
Moreover, since the frequency characteristics of the conventional digital filter designed by Weaver method are limited by the band ratio, the phase error, and the filter order, it is difficult to change the characteristics of the digital filters or make them variable in the filter of design or use, and accordingly it is difficult to change the characteristics of the 90-degree digital PSN or to make them variable.
In the case of a linearizer, moreover, a RZ-SSB (Real Zero SSB) system as an improvement of the conventional SSB (Single Side Band) system has been proposed. This system is characterized in that an AGC (Automatic Gain Control) circuit and an AFC (Automatic Frequency Control) circuit, which are employed in the conventional SSB system, are not necessary, and that the system has a higher fading resistance than the conventional SSB system.
Here, the RZ-SSB system will be explained.
Where a signal having its band limited is represented by g(t) and its Hilbert transformation is represented by g.andgate.(t), an LSB signal s(t) of a full carrier SSB is expressed by the following equation: EQU s(t)=A.sub.c [(1+M.multidot.g(t)).multidot.cos (.omega..sub.c t)+M.multidot.g#(t).multidot.sin (.omega..sub.c t)] (1)
where A.sub.c and .omega..sub.c represent the amplitude and the angular frequency of a carrier, respectively, and M (0.ltoreq.M&lt;1) a modulation index.
From the equation (1), the following equations (2) to (5) are obtained: EQU s(t)=A(t).multidot.cos .theta.(t) (2) EQU A(t)=A.sub.c [(1+M.multidot.g(t)).sup.2 +(M.multidot.g#(t)).sup.2 ].sup.1/2( 3) EQU .theta.(t)=.omega..sub.c .multidot.t-.omega.(t) (4) EQU .omega.(t)=tan.sup.-1 [M.multidot.g#(t)/(1+M.multidot.g(t))](5)
The signal expressed by the equation (2) can be demodulated by the use of a demodulation circuit as shown in FIG. 2.
An input signal .nu. (t) to a linearizer shown in FIG. 2 is given by the following equation, which is an expansion into power series of M (&lt;1): ##EQU3##
The output y(t) of the conventional linearizer using the Hilbert transformers can be given by EQU y(t)=.nu.(t)-.nu.(t).multidot..nu.#(t)+.nu.(t).multidot.(.nu.#(t)).sup.2 /2-(.nu.#(t)).sup.3 /6. (7)
In the equation (7), y(t) represents an output of the linearizer. Theoretically, when the signal .nu. (t) has been input into the linearizer, the output y(t) given by the following equation (8) is obtained. That is, a Hilbert-transformed primitive signal g#(t) and a distortion O(M.sup.4) of a negligible level indicated by a four or more dimensional term are output. EQU y(t)=M.multidot.g#(t)+O(M.sup.4) (8)
The linearizer whose output is given by the equation (8) has a structure as shown in FIG. 3.
Since the Hilbert transformers shown in FIG. 3 have a rather complicated structure, the overall circuit of FIG. 3 is actually very complicated.